CPM Homework Help : PCT Problem 4-73

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4-73.

Simplify the following rational expressions into a single fraction.

$\frac { x } { y } - \frac { y } { x }$
Hint (a):
Multiply the first fraction by $\frac{x}{x}$ and the second fraction by $\frac{y}{y}$ to get a common denominator.

$( \frac { 1 } { x } - x ) ( \frac { 1 } { x } + x )$
Hint (b):
Multiply out. Get a common denominator.

$\frac { ( 1 / y ^ { 2 } ) - 1 } { 1 / y ^ { 2 } }$
Hint (c):
The bottom fraction flips to the numerator:
$\left(\frac{1}{y^2}-1\right)\left(y^2\right)$
Distribute and simplify.

$\frac { 1 } { x - y } + \frac { 1 } { x + y }$
Answer (d):
$\frac{2x}{x^2-y^2}$
Show all of your steps.

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